According to Rev. Shepherd in "The History of Kirby Underdale," Benjamin's twins were Lillie Mary & Florence Effie. However, they are not with the family in the 1880 census, so may have died young.
In the Federal Census of 1860, Frank & Mary Remington, ages 34 and 36, are living at New York City. Frank is a Baptist clergyman. Daughter Florence is 4; Mary is 2.
In the 1870 Federal Census, Frank & Mary Remington and family are at East Cleveland; the children's names appear to be Mary, Grace K., & Henry. In the 1880 Federal Census, Frank & Mary Remington and family are living in District 51, Cleveland, Cuyahoga Co., OH. The children's names appear to be May A., Grace K., & Harry H.
I am not sure of the exact dates of all the children in this family (needs more research).